Question

The equivalent stiffness of the system as shown in the figure below is

• A. $0.6\times {10}^5\text{N/m}$
• B. $1.18\times {10}^5\text{N/m}$
• C. $2.35\times {10}^5\text{N/m}$
• D. $4.69\times {10}^5\text{N/m}$

Answer 1

The correct option is D $4.69\times {10}^5\text{N/m}$

Equivalent stiffness of cantilever beam having load at free end,

$k_b=\frac{3EI}{L^3}=\frac{3\times (210\times {10}^9)\times (1.5\times {10}^{-5})}{(2.5{)}^3}$

$=6.05\times {10}^5\text{N/m}$

The beam and upper spring act is parallel.
This parallel combination is in series with the spring placed between the block and the beam. Further this series combination is in parallel with the spring placed between the block and the surface.

$k_{eq}=\frac{1}{\frac{1}{(6.05\times {10}^5)+(5\times {10}^5)}+\frac{1}{2\times {10}^5}}$

$=4.69\times {10}^5\text{N/m}$